Cremona's table of elliptic curves

575 = 5² · 23

Field	Data	Notes
Atkin-Lehner	5- 23-	Signs for the Atkin-Lehner involutions
Class	575d	Isogeny class
Conductor	575	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	8984375 = 58 · 23	Discriminant
Eigenvalues	-1  0 5-  1 -1  1  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-55,72]	[a1,a2,a3,a4,a6]
Generators	[-6:15:1]	Generators of the group modulo torsion
j	46305/23	j-invariant
L	1.4098509775926	L(r)(E,1)/r!
Ω	2.0499620939546	Real period
R	0.22924830037107	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9200be1 36800bp1 5175p1 575a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 575d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	0	-	1	-1	1	0	-5	-	-5	-2	-4	-5	-9	-6	2	8	-8	8	-10	-3	-3	3	10	-2

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Quadratic twists for elliptic curve 575d1

-4	8	-3	5	-7	-11	13	-23
9200be1	36800bp1	5175p1	575a1	28175bc1	69575ba1	97175s1	13225g1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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